Triangle inequalities in international trade: The neglected dimension

Estimating trade costs is key to understanding the welfare effects of trade liberalizations. Cost minimization implies that the triangle inequality (TI) of international trade costs must hold for any three countries to avoid cross-border arbitrage. We show that re-routing opportunities might arise when trade costs change because a shipment through an intermediary becomes cheaper. The TI captures such re-routing opportunities. However, standard approaches to calculating the gains from trade liberalizations ignore this no-arbitrage condition. We outline an estimation routine that is model-consistent and respects the TI. Counterfactual exercises suggest that the welfare gains from re-routing after trade liberalizations can be substantial. • Triangle inequality (TI) of trade costs often violated in standard estimates. • TI violations affect the validity of exact hat algebra. • Provide a simple routine to obtain TI-consistent trade costs. • Accounting for re-routing matters for welfare gains. • Build a bridge to the economic geography literature.